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x^2-x-6=7
We move all terms to the left:
x^2-x-6-(7)=0
We add all the numbers together, and all the variables
x^2-1x-13=0
a = 1; b = -1; c = -13;
Δ = b2-4ac
Δ = -12-4·1·(-13)
Δ = 53
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{53}}{2*1}=\frac{1-\sqrt{53}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{53}}{2*1}=\frac{1+\sqrt{53}}{2} $
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